I'm new to learning foreign languages (I took Spanish and German in middle and high school, but wasn't serious about them) and this might be something obvious to people with experience translating.
I'm learning Homeric Greek right now, but I know αὐτός appears in Classical Greek as well, so it might not be just a problem with Homeric.
I was working on an exercise and came across this sentence:

"δῖος ἑκηβόλος αὐτὸς αείδει , ἀλλ' οὐχ ἁνδάνει ἄλλοισι θεοῖσι θυμῷ."

I translated it as

"The godly sharpshooting one sings, because he is pleasing to the gods' selves in the souls."

I guess the trouble is αὐτὸς. I'm not sure how it works here. Is it just acting like a third person pronoun? Is it supposed to be translated or just to kind of point out the fact that the sentence is talking about he, the godly sharpshooter?

"The godly sharpshooting one sings, because he is pleasing to the gods' selves in the souls."

I've discovered via google search which led me to another forum that this line
is from Pharr's Homeric Greek Lesson 8. The vocabulary at the beginning lets you know that
ἀλλά (here ἀλλ' due to initial vowel in the following word) means but, (moreover),
not because. αὐτὸς is merely for some emphasis as αείδει already established it is Apollo
who is singing. It is usually translated as himself in such sentences.

"The divine sharp-shooter (Apollo) himself sings, but it is not pleasing the hearts of the other gods."
(lit. to the other gods in the heart.)

Nate's translation looks good to me. The important point is that the use of αὐτός in Homeric Greek is very different from Attic or Koine, where αὐτός is often just a third person pronoun - in Homeric Greek it has more emphasis and means himself or the like, according to context.

In Homeric Greek, where in later Greek you would have αὐτός, you often have what is called "the article":

τὴν δ' ἐγὼ οὐ λύσω "(And/but) I will not release her" (Iliad book 1 line 29)

It's a bit misleading to call τὴν an article, since in Homeric Greek it's more like a demonstrative pronoun. But since it in later Greek it became the article, it's called like that.

Nate has it right. autos is like Latin ipse, Apollo himself sings, he sings in person. This usage is universal in Greek, from Homer through Attic and koine on. Paul's point risks muddying the waters, for it applies not to autos but to the oblique cases of the pronoun (in Attic auton = either ipsum or eum; in Homer the latter would be ton). The sentence is a very bad one, quite unGreek.

I skipped the second half of the sentence, but there's no "because" and nothing about "the gods' selves."
"(The) divine far-shooter himself sings, but does not please (the) other gods in their heart."
HTH